In our previous article we took a peek behind the curtain of the SWAPCURVE function gaining insight into the mechanics of turning cash rates, Eurodollar futures prices, and swaps rates into discount factors and continuously compounded zero coupon rates. In this article we attempt to do a little reverse engineering to see if it's possible to take those discount factors and turn them back into the supplied inputs or their associated spot rates.

The XLeratorDB table-valued function SWAPCURVE takes cash, futures, and swaps rates as input and returns discount factors and continuously compounded zero coupon rates which can then be used in a variety of sophisticated financial calculations. In this article we take an in-depth look at the mechanics of SWAPCURVE calculation using SQL and other XLeratorDB functions to explain where the numbers come from. These alternative calculations are designed to be explanatory and not as a substitute for the SWAPCURVE function which will be, by far, the fastest and easiest way to generate the curve values.

XLeratorDB was developed to provide the best possible in-database analytics capability for SQL Server and we continue to believe that the best platform for doing sophisticated analytics on large datasets is SQL Server with XLeratorDB. Over the last 8 years, however, non-SQL Server users were also interested in having many of these functions and even some SQL Servers preferred the XLeratorDB functions in non-database applications. We are happy to announce the availability of XLeratorDLL/financial and in this article talk about the advantages of using this library in your .NET code and why should really never use Microsoft.Office.Interop.Excel,Worksheetfunction for financial calculations.

Current Expected Credit Loss (CECL) is coming soon. In this article we talk about new functionality that we have added to XLeratorDB to makes loan level cash flow modeling simple. Using our new table-valued function CDRCASHFLOW in SQL Server you can create extremely sophisticated models using some very simple SQL which scales up for hundreds of thousands if not millions of individual loans. If your data already resides in SQL Server, you can implement this functionality without making any changes to your existing applications.

The XLeratorDB financial library contains more than three dozen functions related to the calculation of price, yield, and accrued interest on bonds, bills, and notes. Recently, one of our customers came to us to help him solve for the yield on a bond which incorporated a tax rate. As with most requirements for financial calculations, he attached a very complicated spreadsheet which contained the underlying math used in the local market to calculate the price from yield for the bond, including the tax rate.

Our original blog on Calculating percentiles in SQL Server, published in 2011, is one of the most popular pages at westclintech.com. In this article, we talk about a table-valued approach to calculating percentiles which in some situations may improve performance dramatically over the PERCENTILE aggregate function.

Calculating internal rates of return for many accounts or portfolios across many different time horizons is a laborious and error-prone task in a spreadsheet and the calculations are easily broken when new cash flows are added. In this article we look at how doing this calculation in SQL Server with just a few lines of SQL lets you calculate internal rates of return for millions of cash flows across all of your accounts or portfolios across multiple time horizons in just a few seconds.

There are a lot of financial calculations that compute 'returns'. There are internal rates of return, return on investment, time-weighted rate of return, multiples of invested capital, compound annual growth rate, and many more. The good news is that you can perform all these calculations in SQL Server using XLeratorDB.
In this article we explore the difference between the two return calculations that we get the most questions about: internal rate of return and total return. You won't need an MBA in Finance to understand these examples; just follow along with SQL Server Management Studio and you will very quickly see how these calculations differ.

XIRR is one of XLeratorDB's most popular financial functions. At Westclintech, we get more inquiries about XIRR than all of the other 200+ financial functions combined. To create a reliable version of XIRR for SQL Server we had to create, quite literally, millions of different test cases which were then tested against Excel.

One technique for creating test cases was to generate all the cash flows except the first one, then make the first cash flow equal and opposite in sign to the discounted cash flow value, or net present value, of all the other cash flows at some discount rate and check to if the internal rate of return, as calculated by the Excel XIRR function, is equal to the discount rate.

Mathematically that technique is absolutely sound, yet we discovered that Excel was not at all reliable in producing the expected result. In this article we share with you what we found.

Diversification is the basis for any sound investment strategy and the heart of diversification is finding uncorrelated risk in different asset classes. In this article we show you how to do that using the XLeratorDB table-valued function CORRM.

We have added 5 new functions to help you calculate internal rates of return (IRR) for a variety of day-count methods. Used in conjunction with our other day-counting functions, you can calculate IRR using actual/actual, actual/360, actual/364, business days / 252, no-leap-year / 365 and others as well as for 30/360.

We have added 5 new functions in the latest release of XLeratorDB / statistics 2008. Four of these functions, LOGIT, LOGITSUM, LOGITPRED, and LOGITPROB are SQL Server implementations of the logistic regression, often referred to as the logit regression. The remaining function, VIF, estimates the variance inflation factor, tolerance, and R2 for a set of independent variables allowing you to test for collinearity.

Bonds with an odd last coupon will arise infrequently in any portfolio. With XLeratorDB you can be confident that when they do show up in your portfolio you will be able to do all the necessary calculations just as easily as you can for bonds that pay regular periodic interest.

In this article we look at shares which pay a quarterly dividend to the preferred shareholders and which are callable at some future date and discuss various techniques for calculating a yield-to-call and explain why using the YIELD function isn't one of them.

We added 7 new table-valued functions to XLeratorDB/financial and XLeratorDB/financial 2008 that generate principal and interest payment schedules for different types of loans. This article provides insight into some of the calculations used in these new functions.

We have previously written about calculating price, yield, and accrued interest for bonds that have regular periodic coupons. However, not all bonds fit that description. Some bonds have an odd first period, meaning that the first coupon period is either shorter or longer than all the other coupons. In this article we will discuss how that affects the calculation of price, yield, and accrued interest and why you should not use the Excel functions for these types of calculations.

We look at some of the math behind the calculation of the price of a bond with regular periodic coupons, talk about how yield and accrued interest are calculated, and make some comparisons between the Excel functions and the XLeratorDB functions. We also talk about 2 new function that we have added to XLeratorDB that make it easier to see how PRICE and YIELD functions came up with their results.

In this article we look at the Excel ACCRINT function, exploring the results returned by the function when it is used as documented, as well as looking at some ways of manipulating the input data so that you can get the result that you want, or at least a result that you can understand, and why you should be afraid of that data manipulation.

As a follow up to our article on calculating a variance – covariance matrix in SQL Server, we look at a similar calculation to produce a correlation matrix and provide 2 relatively straightforward methods for calculating the correlation matrix in SQL Server, using the XLeratorDB function library, and compare them to the calculation provided in the Excel Data Analysis tool.

In this article we look at 2 relatively straightforward methods for calculating a variance-covariance matrix in SQL Server, using the XLeratorDB function library, and compare them to the calculation provided in the Excel Data Analysis tool.

The latest release of XLeratroDB/math contains 5 new functions for numerical integration, 12 new functions for the generation of non-uniform random numbers and, for users of SQL Server 2008 and above, 2 new functions for calculating the nth MIN or nth MAX of a data set.

In the latest release of our math library (1.09) we introduce 5 new functions for numerical integration in SQL Server. In this second of two articles we follow up on some of the concepts behind numerical integration focusing specifically on integration over semi-infinite and infinite intervals. We will explain some of the general concepts behind numerical integration, also called quadrature, using Simpson's rule, and then look at functions for Gaussian and Double Exponential quadrature.

In the latest release of our math library (1.09) we introduce 5 new functions for numerical integration in SQL Server. In this article we explore some of the concepts behind numerical integration and discuss the different techniques used in the new functions, focusing specifically on integration over finite intervals. We will explain some of the general concepts behind numerical integration, also called quadrature, using Simpson's rule, and then look at functions for Gauss-Kronrod, and Tanh-Sinh quadrature. In Part 2, we will look at integration over semi-infinite and infinite intervals.

In this article we talk about the XLeratorDB GROWTHMX and LOGEST functions, compare them with the TRENDMX and LINEST functions, and describe some techniques to turbo-charge your predictive analytics in SQL Server.

We have added a new function, MONOSPLINE, to the XLeratorDB/math 2008 library based on "Monotone Piecewise Cubic Interpolation," by Fritsch, F. N. and R. E. Carlson, SIAM J. Numerical Analysis, Vol. 17, 1980, pp.238-246. In this article we look at how the MONOSPLINE function works on monotonic data and compare it to linear, natural cubic spline, and polynomial interpolation in SQL Server.

We have added new functions for calculating the statistics of inter-observer agreement, as well as enhancing existing aggregate functions which calculate descriptive statistics like variance, standard deviation, covariance, etc.

With the release of SQL Server 2012, SQL Server users were finally able to use aggregate functions in a window, enabling calculations like running sums and moving averages. XLeratorDB/windowing put these capabilities into SQL Server 2005 and SQL Server 2008 as well as providing dozens of calculations that are not available in SQL Server 2012. With our latest release of XLeratorDB/windowing we add 14 new functions to the 38 existing functions.

The latest release of XLeratorDB / finance contains a bunch of new functions for yield curve construction, 2 new bond pricing functions, and an addition to the list of Capital Asset Pricing model formulas.

With the release of XLeratorDB/windowing 1.01 we introduce three new functions for calculating inventory values: FIFO; LIFO; and WAC. These functions calculate the quantity-on-hand, cost-of-goods sold, gross margin, and inventory value using the First In, First Out (FIFO), Last In, First Out (LIFO), or Weighted Average Cost (WAC) method. In this article we talk about how those calculations work and how you can incorporate these calculations into T-SQL statements without having to do a self-join.

In this article we look at how moving a traditional spreadsheet calculation into SQL Server simplifies the calculation while also allowing you to analyze more data in more different ways than you would think possible

XLeratorDB / financial 1.10 contains 19 new functions: 3 functions for calculating time-weighted rate of return; 9 new functions for calculating some popular Capital Asset Pricing Model (CAPM) ratios; 3 new functions for calculating the interest rate sensitivity of a series of irregular cash flows; 2 new functions for calculating dates; a function for calculating multiple of invested capital; and a new function for calculating discounted cash flows.

SQL Server 2012 added more complete support for window functions, including enhanced support for window aggregate functions, as well as support for window offset and window distribution functions. In our latest function library, XLeratorDB / windowing, we make many of the same capabilities available for SQL Server 2005 and SQL Server 2008 users, as well as providing a bunch of functions that aren’t available in SQL Server 2012, but are available in Oracle.

The modified Dietz calculation produces a result which measures the performance of an investment portfolio based on time-weighted cash flows. Today, we will look at two XLeratorDB aggregate functions, EMDIETZ and FVSCHEDULE, which calculate the modified Dietz value for each period and then link the results together to come up with a time-weighted rate of return value.

With the release of our newest library of functions, XLeratorDB/financial-options, you have the ability to calculate the price and Greeks for American and European options in SQL Server 2005, 2008, and 2012. This release includes the Black-Scholes-Merton pricing formula, the Bjerksund & Stensland 2002 American approximation, and binomial trees for American and European options. It also includes calculation of the implied volatility and some table-valued functions and stored procedures for analyzing the price and P&L impacts of changes in the underlying asset price, the volatility, the risk free rate, and time decay.

Release 1.09 of XLeratorDB / financial and XLeratorDB / financial 2008 contains 5 new date functions: BUSDAYS, BUSINESSDATE, BUSINESSDATEWE, DAYS360 and DAYSNL. In this article, we explore how these functions work and the kinds of calculations that can now easily be done in your SQL Server database.

We introduce seventeen useful new functions which help analyze accrued interest on bonds, create payments schedules for commercial loans and leases, calculate dates and the number of days between two dates incorporating weekends, holidays, and day-count conventions, and perform time value of money calculations when there is an odd first period.

A look at different techniques for generating schedules to account for the premium or discount associated with the issuance or purchase of a bond using the XLeratorDB functions COUPDAYSNC, COUPNUM, DAYS360, EDATE, IRR, PRICE, PV, RATE, SeriesDate, SeriesInt, XIRR, and YIELD.

We have added some performance enhancements to the pseudo-random number generators, as well as a new function to generate random normal numbers.

We created scalar versions of the table-valued matrix functions, making the SQL much simpler and easier to follow. We also added a couple of new matrix functions for forward substitution and back substitution.